We develop a normal form to express asymptotically a conjugacy between a germ of resonant vector field and its linear part. We show that such an asymptotic expression can be written in terms of functions of the Logarithmic Mourtada type. To cite this article: P Bonckaert et al., C. R. Acad. Sci. Paris, Ser. I336 (2003). (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.